Factor completely the polynomial. Indicate any that are not factorable using integers. x ² - 10 x + 21 A)( x + 3)( x + 7) B)( x + 3)( x - 7) C)( x - 3)( x - 7) D)( x - 3)( x + 7) E)not factorable

Question

Quizplus · Accepted Answer

We can use the AC method or grouping to factor. The product of the first and last coefficients is 1 * 21 = 21. The factors of 21 are 1 and 21 or 3 and 7. We want to find a sum or difference of these factors that gives us the middle coefficient of -10. We can try -3 and -7, which sum to -10, so we use those as our factors. Then, we can regroup the terms:
x(x-7) - 3(x-7)
We can then factor out the common factor of (x-7) to get:
(x-7)(x-3)
This is the fully factored form, which matches choice C.

Factor Completely the Polynomial